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Climate and Weather of the Sun-Earth System (CAWSES): Selected Papers from the 2007 Kyoto Symposium, Edited by T. Tsuda, R. Fujii, K. Shibata, and M. A. Geller, pp. 201–216. c TERRAPUB, Tokyo, 2009. Evidence for solar forcing: Some selected aspects Jürg Beer1 and Ken McCracken2 1 Eawag, CH-8600 Duebendorf, Switzerland E-mail: [email protected] 2 Institute for Physical Sciences and Technology, University of Maryland, College Park, Maryland, USA It is believed that the global warming since the mid-20th century is primarily the result of the combustion of fossil fuel. The fact that the climate also changed in the past during periods of rather constant atmospheric greenhouse gas concentrations points to additional factors such as solar and volcanic forcing. The Sun is by far the most important source of energy for Earth and direct satellite based observations during the past 30 years show that the solar constant (total solar irradiance TSI) changes in phase with the solar magnetic activity. The past 30 years are characterized by a high, rather constant mean level of activity, however, during the last 2 years the minima in TSI, IMF (interplanetary magnetic field), NM (neutron monitor count rate), and (solar modulation function) have clearly deviated from the earlier minima, suggesting that TSI is now decreasing in response to a lower level of solar magnetic activity. Unfortunately our knowledge of past solar activity is very limited, the longest record available being the sunspot record going back to 1610. The record can be extended from centuries to millennia by using the cosmogenic radionuclides which are primarily produced by the galactic cosmic rays. Their intensity is modulated by the open solar magnetic and the geomagnetic field. Removing the geomagnetic effects results in the solar modulation function which can be reconstructed for the past 10,000 years, as can the strength of the interplanetary magnetic field. The comparison of with selected climate records provides strong evidence that solar forcing was important in the past and will possibly play a role in the future. Confirmation of the synchronous declines in TSI and IMF will allow the reconstructed IMF to be used to estimate TSI for the past 10,000 years. 1 Introduction In the recently published IPCC report (Solomon et al., 2007) the authors conclude that the available evidence is now strong enough to state that “Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations”. This means that the global change observed during the past few decades is outside the range of expected natural variability, or in other words, it cannot be explained as a result of natural forcings. It is important to note that this statement does not mean 201 202 J. Beer and K. McCracken that without anthropogenic forcing the climate would stay unchanged in the future. The climate has always changed and will continue to do so in the future. As a consequence the predictions of the impact caused by anthropogenic activities on future climate change must allow for the natural variability. The climate is a dynamic non-linear system of large complexity that varies on time scales from months to millions of years. It is an open system and interacts with space through electromagnetic radiation, matter in the form of galactic and solar cosmic ray particles, and magnetic fields. By far the strongest interaction takes place with the Sun which is the most important source of energy. The power from cosmic ray particles is in the order of 109 W which is comparable to the power received by the stars during the night. However, the total power of solar radiation arriving at the top of the atmosphere is about 8 orders of magnitude larger and amounts to 2 1017 W. Processes of reflection, absorption, distribution, and emission control the flow of solar radiation, with the climate system attempting to equilibrate the temperatures and to reach an equilibrium between incoming short wave radiation and out going long wave radiation. As a consequence the conditions at the Earth’s surface depend strongly on the amount of incoming solar radiation (Total Solar Irradiance TSI), its spectral distribution (Spectral Solar Irradiance SSI), the atmospheric composition (greenhouse gases, aerosols), the albedo (clouds, ice and snow, vegetation), and the internal variability caused by the transport processes redistributing the energy (ocean and atmospheric circulation and latent heat transport). Some of these have long time constants with the consequence that the responses to external forcings may be long delayed. The fact that the climate is a complex non-linear system makes it difficult to obtain a quantitative understanding of its temporal and spatial variability in the past. This makes it especially difficult to make reliable predictions about the future. A good example of the difficulties we face when dealing with the climate system is provided by the modern weather forecast. Even today, with an almost unlimited amount of information from weather stations and satellites, and with the most advanced general circulation models (GCM’s), it is impossible to make reliable predictions beyond about seven days. In spite of all our impressive technological progress, the chaotic properties of the weather system will always prevent us from making detailed and accurate long-term predictions. One could therefore come to the conclusion that understanding climate change is hopeless. However, it seems that many of the short-term chaotic climate fluctuations are averaged out when going to time scales of decades and larger and that a limited set of parameters exists which if known well enough will enable us to make useful predictions. We are therefore faced with two distinctly different problems. (1) To understand how the climate system works, and to determine the parameters, that best determine its secular changes, and (2) to be able to predict the magnitude of the natural and anthropogenic forcings in the future. Probably the best way to address the first problem is to improve our understanding of the longer-term dynamics of the climate system by studying the history of past natural forcings and the corresponding responses of the climate system. Based on this information more reliable predictions about future Evidence for Solar Forcing 203 Fig. 1. Increase in solar luminosity relative to the present (L = 1). Note that a billion years after the formation of the solar system the luminosity was more than 20% smaller than today. natural forcing changes can be made. In the case of the second problem, the anthropogenic forcings scenarios of e.g. greenhouse gas emissions can be constructed which are based on certain assumptions about the future development of the world’s population and its economy and technology. Even though the increase in greenhouse gases is going to be the dominant factor in climate forcing during the coming decades, natural forcing will continue to play a role. In the following we will focus on some aspects related to solar forcing. 2 The Source of the Sun’s Emissions Since the Sun is by many orders of magnitude the most important source of energy it is quite reasonable to assume that any change in TSI and SSI will affect the climate on Earth. Such changes can have very different causes and may occur on very different time scales. The fusion of hydrogen to helium takes place in the core of the Sun where every second some 4.2 Million tons of mass are turned into electromagnetic radiation. According to the standard solar model this process is very stable but increases monotonically from L≈0.8 three billion years ago to L≈1.3 in 3.5 billion years time (Fig. 1), when the sun will run out of hydrogen and first turn into a red giant and then into a white dwarf. The change in luminosity at present is only 7 10−11 per year and therefore completely irrelevant for climate changes on time scales of centuries and millennia. Nevertheless, the dramatic change on a billion year time scale raises the interesting question how planet Earth avoided becoming a “snowball” in its young age. This question is often called the “faint young sun paradox” (Sagan and Chyba, 1997). On its way to the Sun’s surface the electromagnetic radiation is repeatedly absorbed and reemitted which steadily shifts the wavelength towards longer values which in turn increases the probability for absorption. At about 2/3 of the Sun’s radius radiative transport becomes so inefficient that the thermal gradient gets very 204 J. Beer and K. McCracken large and convection sets in. Most of the solar power is radiated into space by the photosphere, a layer of thickness about 500 km, at a temperature of 5770 K. The spectrum of the emitted light can be approximated in a first order by the Planck spectrum of a black body at this temperature. To date, not much attention has been paid to the question whether the energy transport from the core to the sun’s surface is subject to variability. Although there are ideas under development how fluctuations in the convection zone might occur (Kuhn et al., 1988; Sofia and Li, 2004; Steiner and Ferriz-Mas, 2006) so far no evidence is available and many arguments are put forward against such fluctuations (Foukal et al., 2006). It is important to note, however, that even small changes in the solar diameter could lead to a significant change in luminosity (Sofia and Li, 2006). 3 Emission from the Surface The emission from the photosphere is what we see from Earth. For a long time the total emission was considered to be constant and it is still often called the “solar constant”. However, there is a long history of investigations to determine whether the solar constant is really constant (Langley, 1903; Abbot, 1910). Unfortunately, fluctuations in the atmospheric opacity prevented these pioneering investigators from proving that the solar constant is not constant. The ability to observe the Sun from satellites ultimately yielded the precision necessary to detect changes in TSI smaller than 0.1%. Figure 2 shows the compilation of TSI measurements which has been carefully put together from different satellites after correcting for various effects such as degradation of the instruments with time (see Fröhlich, this volume). Many attempts have been made to explain the observed fluctuations of TSI. The principle of most approaches is to separate the solar disc into several components such as a background component considered as constant, a negative component given by the dark sunspots including umbra and penumbra and a positive component consisting of the bright faculae and the magnetic network. By weighing these different components accordingly with the so-called filling factor the measured TSI fluctuations can be reproduced surprisingly well for the period 1980–2004 (Wenzler et al., 2006; Krivova et al., 2007). In spite of this success this approach has the inherent disadvantage that it is basically a regression model, which is based to a large extent on observations (filling factors) that are only available for the recent past. In particular, it provides no information on the variability of the background component on decadal to centennial time scales; these being most relevant as far as climate forcing is concerned. It has been long recognized that the variability of TSI must be closely linked to the magnetic activity of the Sun (Baliunas and Jastrow, 1990). The factor of three reduction in solar forcing in the IPCC4 report was primarily due to a reassessment of the long-term changes in properties of the solar magnetic fields between the Maunder Minimum and the present. The strength of the interplanetary field near Earth is closely related to the magnetic fields on the Sun (Wang et al., 2000), and is plotted in Fig. 2. Both TSI and IMF exhibit 11 year variations, a 0.4 W m−2 change in TSI corresponding to a 1.0 nT change in IMF. While the strength of the IMF at the three [MeV] Neutrons [cpm] IMF [nT] Sunspots -2 TSI [W m ] Evidence for Solar Forcing 1368 1367 1366 1365 1364 150 100 50 0 10 8 6 4 5000 5500 6000 6500 1000 205 a b c d e 500 0 1975 1980 1985 1990 1995 Year 2000 2005 2010 Fig. 2. (a) Composite of TSI measurements during the period 1978 until 2008 compiled by C. Fröhlich (daily data). (b) Sunspots (monthly data) (c) Interplanetary magnetic field (daily data) (d) count rate of the neutron monitor from Oulu (daily data on a reversed y-axis) (e) Solar modulation function derived from neutron monitor data (monthly data). previous sunspot minima was ∼5.2 nT, we note that it decreased through that value in the first half of 2006 and decreased steadily to a mean of ∼4.25 nT in late 2007. In exactly the same manner, TSI decreased below the previous minimum values in early 2006, and was ∼0.4 W m−2 lower by late 2007 probably pointing to a long-term change in the background contribution. While the first direct measurements of the IMF started in the 1960s, three methods have been used to extrapolate the present day values to the past, these being used to some extent in IPCC4 as a proxy for TSI. The cosmogenic nuclides are the basis of one of those methods, and are unique in their ability to provide estimates of the IMF over the previous millennia, offering the possibility to estimate TSI far into the past. 4 The Cosmogenic Nuclides and the IMF as Proxies for TSI The production rate of the cosmogenic nuclides (e.g. 10 Be and 14 C) is modulated by the open magnetic field which is carried away from the Sun by the solar wind (see below) (McCracken and Beer, 2007). 10 Be from ice cores and 14 C from tree rings, 206 J. Beer and K. McCracken 10.0 HELIOMAGNETIC FIELD (nT) 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 1400 1500 1600 1700 YEAR 1800 1900 2000 Fig. 3. IMF derived from 10 Be for the past 600 years. (From McCracken, K. G., Heliomagnetic field near Earth, 1428–2005, J. Geophys. Res.—Space Phys., 112, A09106, 2007. Copyright 2007 American Geophysical Union. Reproduced by permission of American Geophysical Union.) together with other cosmogenic radionuclides, provide our only continuous record of the long-term variability of solar activity prior to the commencement of the sunspot record in 1610. They also constitute a cosmic magnetometer that provides estimates of the strength of the IMF for the past 10000 years. As an example, Fig. 3 presents the strength of the IMF for the past six centuries derived from the 10 Be data (McCracken, 2007). Note the estimated field strengths of ≤1 nT for the Spoerer and Maunder Minima. Note also the ∼85 year variability (the Gleissberg Cycle). It appears possible that the decreasing field after 2006 in Fig. 2 may be the commencement of another period of reduced field strength similar to ∼1815 or ∼1900, with implications for a lower TSI. Cosmogenic radionuclides are produced by nuclear interactions of the galactic cosmic rays (GCR) with atoms (N, O, Ar) in the atmosphere. To reach the atmosphere the GCR have to propagate through the heliosphere which forms a bubble with a radius of about 150 Astronomical Units (AU) around the Sun that is filled with solar plasma carrying magnetic fields (Fig. 4). The propagation of the cosmic rays is described by the transport equation derived by Parker (Parker, 1965). It is difficult to use the transport equation to parameterize the intensity of the GCR, however the so-called force field approximation (Gleeson and Axford, 1967) has proven to be a good approximation near Earth. This approximation describes the modulation effect of the Sun on the energy spectrum of the GCR in terms of a parameter called the Evidence for Solar Forcing 207 Fig. 4. Voyagers 1 and 2 have flown on different trajectories past the outer planets of the solar system since 1977, and Voyager 1 crossed the termination shock of the solar wind at 94 AU from the Sun in December 2004. Voyager 2 did likewise in 2007. The solar wind is a supersonic flow, and a shock—the termination shock—is required for the wind to decelerate and merge with the local interstellar medium that bounds the solar system. The solar wind and interstellar gas do not merge easily, so further out beyond the termination shock, there is a thick boundary region between the solar wind and the interstellar medium: the heliosheath. Further out still, if the solar system is itself moving supersonically relative to the interstellar medium, there may be a large bow shock. (From Fisk, L. A., Journey into the unknown beyond, Science, 309, 2016–2017, 2005. Reprinted with permission from AAAS.) solar modulation function. basically corresponds to the average energy lost by a cosmic ray proton on its way to the Earth. Figure 5 shows the differential energy spectrum of the GCR proton flux for different levels of solar activity. = 0 MeV corresponds to the local interstellar spectrum outside the heliosphere (Fig. 4). This spectrum is an estimate because no space probe has left the heliosphere yet and actually measures this spectrum. Voyager 1 and 2 have crossed the termination shock and are passing through the heliosheath (Fig. 4). Figure 5 shows that the shielding effects of the solar open magnetic field are most pronounced at the low energy end of the spectrum. As a consequence GCR particles above about 20 GeV are hardly affected by the heliospheric magnetic fields. Before reaching Earth the cosmic ray particles have to overcome a second barrier, the geomagnetic field. This field prevents particles with too low a rigidity (momentum per unit charge) from reaching the top of the atmosphere. In a first approximation the geomagnetic field is considered as a dipole and in this case the cut-off rigidity depends only on the angle of incidence and the geomagnetic latitude. At low latitudes the cutoff rigidity for vertical incidence is presently ∼14.9 GV. This means that a cosmic ray 208 J. Beer and K. McCracken -1 10 -2 -3 10 -1 -1 Protons [cm MeV s ] 10 -4 -2 10 -5 10 0 100 200 400 600 1000 2000 -6 10 -7 10 -8 10 1 10 2 10 3 10 E [MeV] 4 10 10 5 Fig. 5. Differential GCR proton fluxes for different levels of solar activity ranging from = 0 MeV corresponding to the local interstellar spectrum arriving at Earth without any solar influence, to = 2000 MeV which corresponds to a very active Sun. There are similar curves for cosmic ray alpha particles and heavier nuclides. The vertical bands illustrate the effect of the geomagnetic field which cuts of all protons approaching vertically with an energy below about 100 MeV for a geomagnetic latitude of 65◦ ; below 1 GeV for 55◦ , and below 3 GeV for 45◦ . At 0◦ the cut-off energy is 13.9 GeV for the present geomagnetic field. proton needs a kinetic energy of at least 13.9 GeV to reach the top of the atmosphere (see shaded bands in Fig. 5). The solar modulation is a monotonic decreasing function of particle energy (Fig. 5) and consequently the modulation is small near the equator (∼14 GeV) and large at high latitudes which are accessible to the strongly modulated energies near 1 GeV. If a primary cosmic ray particle makes its way through the heliosphere and the geomagnetic field and enters the atmosphere it will interact quickly with an atom of oxygen, nitrogen, or argon. Since the energies of incoming particles are generally very high, only part of their kinetic energy is transferred to the first atom they hit. They continue their travel and hit a few more atoms until their energy is dissipated. Each collision results in the generation of secondary particles covering the full spectrum of hadrons and leptons, which either decay or interact with other atoms of the atmosphere. In this way a cascade of secondary particles develops which can be simulated using the Monte Carlo technique (Masarik and Beer, 1999, 2009). The simulations show that the majority of the secondaries are neutrons followed by protons. Both, in turn, collide with atmospheric atoms initiating spallation reac- Evidence for Solar Forcing 209 tions (Masarik and Beer, 1999; Webber and Higbie, 2003; Masarik and Beer, 2009), that generate the cosmogenic nuclides that are archived for us in ice (10 Be, 36 Cl) or tree rings (14 C). In addition, the cosmic ray produced neutrons have been monitored continuously since 1951 by so-called neutron monitors. In Fig. 2(d) the count rate of the Oulu neutron monitor clearly shows the modulation of the GCR by the 11-y Schwabe cycle (Fig. 2(b)). Whenever the magnetic activity is high (large sunspot numbers) the shielding is strong and the neutron flux is low. As we discussed above the solar modulation of the GCR can be described by the modulation function which is shown in panel e of Fig. 2. Many studies have shown that the 11 yr and longer-term variations are faithfully reproduced in the cosmogenic data, and they and the neutron monitor data have been inter-calibrated to yield a continuous cosmic ray record for the past 10,000 years (McCracken and Beer, 2007; Steinhilber et al., 2008). In practice, the cosmogenic data contain substantial statistical variations, and some residual atmospheric effects. The quality of the solar signal can be improved by combining different 10 Be records from different sites, together with the 14 C record from tree rings. 14 C is produced almost identically as 10 Be, but behaves geochemically in a completely different manner. It forms 14 CO2 which exchanges between atmosphere, biosphere, and ocean. These large reservoirs cause a considerable attenuation of the high frequency production changes and delays while 10 Be is removed from the atmosphere quickly within 1–2 years. Combined together, however, the two cosmogenic nuclides provide a result that is largely devoid of atmospheric or other “system effects”. The cosmogenic radionuclides record the cosmic ray intensity with a relatively low temporal resolution of 1 year compared to a few minutes for a neutron monitor and furthermore, a relatively low signal to noise ratio. However, they have the unique advantage that at present they are the only “neutron monitor” capable of recording the cosmic ray flux on Earth for the past 10,000 years compared to the almost 60 years of modern neutron monitors. This is another example of nature providing its own solution to an engineering problem long before mankind even was aware of the problem. 5 The Long-term Solar Variability Record In the following we describe how the long-term solar variability record is derived, and from it, the estimated strength of the interplanetary magnetic field near Earth. Some of its spectral properties are then discussed, and finally they are compared with some selected examples of climate change, pointing to a significant role of the Sun in the past. As discussed above the 10 Be record reflects changes in the open magnetic field filling the heliosphere, in the geomagnetic dipole field, and to some extent in the transport of 10 Be from the atmosphere where it is produced to the ice sheet where it is stored. GCM models show that the transport effects were relatively stable during the climatic conditions prevailing during the Holocene (the last 10,000 years), so to a first approximation they can be neglected. This is not the case for the geomagnetic field which exhibits significant long-term changes (Muscheler et al., 2005; Vonmoos et al., 2006). 210 J. Beer and K. McCracken 1000 800 600 Φ [MeV] 400 O 200 M W S 0 0 2000 4000 6000 8000 Age [cal years BP] Fig. 6. Solar modulation function from the present (0 BP corresponds to 1950) back to 9350 BP (Steinhilber et al., 2008). The blue curve data is low-pass filtered with a cut-off of 150 years, the red one with 1000 years. The most recent solar minima are indicated: M: Maunder; S: Spoerer; W: Wolf, and O: Oort. Using our Monte Carlo simulations (Masarik and Beer, 1999, 2009), the effects of secular changes of the geomagnetic dipole field have been removed and we are left with the solar modulation function (Fig. 6). The GRIP ice core record is limited to the period from 1640 to 9300 BP and has recently be complemented by the most recent 360 years which are a composite of derived from neutron monitor data and those from a shallow ice core (Steinhilber et al., 2008). The data of Fig. 6 have been low-pass filtered with a 150 y cutoff. The most striking features of the record are the many distinct minima which correspond to grand solar minima such as the Maunder (M), Spoerer (S), Wolf (W), and Ort (O). The fact that never reaches zero means that there is always some residual open magnetic flux; in other words the solar dynamo seems to weaken from time to time, but it never stops. The maxima are less pronounced. It is interesting to note that the present level of solar activity is comparatively high although there were earlier periods with similar or possibly even higher activity around 2000, 4000, and 9000 BP. There is also a clear long-term trend indicated by the thick line that is low-pass filtered with a cut-off of 1000 years. For a more detailed analysis we calculate the power spectrum using wavelet analysis (Grinsted, 2002–2004). Figure 7 shows the wavelet spectrum of . There are several distinct periodicities some of which are listed in Table 1. Since the time scales for 10 Be in ice cores are not as easily established as those for 14 C in tree rings we also give the corresponding periodicities for 14 C (Reimer et al., 2004) and Q14 C calculated for almost the same time interval (1750–9300 BP). Q14 C is the 14 C production Evidence for Solar Forcing 211 Fig. 7. Wavelet analysis (Grinsted, 2002–2004) of the data from Fig. 6. Cycle/Period Hallstatt DeVries, Suess Gleissberg Table 1. 14 C 2194 2275 982 984 207 208 352 350 704 714 497 512 105 105 86 87.9 Q14 C 2424 957 208 350 713 512 105 87.0 rate which was calculated using the Intcal04 calibration curve and the Siegenthaler Oeschger carbon cycle model (Oeschger et al., 1975). An interesting feature of Fig. 7 is that the cycles wax and wane during the Holocene. There are periods when most cycles show large amplitudes (between 2000 and 3000, and between 5000 and 6000 BP) and times when the amplitudes are generally low (between 4000 and 5000 BP). 212 6 J. Beer and K. McCracken Solar Variability and Past Climate Change Finally we address the question whether the reconstructed solar variability correlates with the known climate change in the past, and whether it has the potential to contribute to a better understanding of future climate change. An unequivocal attribution of an observed climate change to a reconstructed change in solar activity is a difficult task. First of all we do not yet know the precise quantitative change in solar forcing in W m−2 . Secondly the response of the climate system is non-linear and can therefore be attenuated, deformed, and delayed with respect to the forcing signal. In addition the climate models show that the response is generally very heterogeneous. Finally the information on a past climate change is based on paleodata usually derived from natural archives such as ice cores, sediments, stalagmites, and tree rings. The usual climate parameters (temperature, precipitation rate) are not directly available but have to be derived from so-called proxies such as the oxygen isotopic ratio 18 O/16 O which, in the case of precipitation, basically measures the temperature at the site where water vapor condenses and forms water droplets. Most proxies are also dependent to some extent on other parameters and have to be calibrated. Therefore the reconstructed climate parameters are subject to uncertainties regarding the climate parameter they represent, but also regarding the time scale. Nevertheless the temporal and spatial resolution of the records is continuously increasing and due to improvements of the existing and the development of new analytical techniques the uncertainties of the data is decreasing. With those caveats in mind, we now examine two examples where it appears that solar forcing has played an important role in climate change long before the recent increase in anthropogenic forcing. We should mention that the literature of such examples is quickly growing and there would be many more examples and maybe more convincing ones. However, we believe that these two illustrate how the modern climate models, together with the reconstructed solar activity, will allow the climate models to be refined, and the proxies such as the modulation function and the strength of the IMF to be calibrated in terms of TSI. The first example concerns the extensions of alpine glaciers. It is a well-known phenomenon that as a result of the present global warming most of the glaciers on the globe are shrinking. Using radiocarbon dating of trees that were killed by an advancing glacier it is possible to reconstruct the history of the glacier’s extension over the past few millennia (Fig. 8) (Holzhauser et al., 2005). Similar observations were made elsewhere (Denton and Karlén, 1973; Hormes et al., 2006). The size of a glacier is mainly related to winter precipitation and summer temperature and integrates over several years to decades. This makes it insensitive to individual weather events and delays its response by a few decades. Figure 8 shows the history of the great Aletsch glacier in Switzerland, the largest glacier in the Alps. The reconstruction shows that it has retreated by more than 3 km since about 1850, and will probably continue to do so. But the figure also shows that the present retreat distance is not unique. It retreated similar distances in the medieval warm period, and at the end of the Roman era, and each time advanced back to where it was in the “little ice-ages”. Comparison with the solar modulation function shows that the advances Evidence for Solar Forcing 213 Fig. 8. Extension of the “great Aletsch glacier” in the Swiss Alps. Photographic records show that the glacier has retreated by more than 3 km since the 19th century. However, the present retreat distance is not unique; similar retreats occurred in Medieval and Roman times. The changes in extension are compared with the curve (Fig. 6) and it is clear that low solar activity corresponded to large extensions of the glacier. correspond in general to low , and retreats to high . It should be mentioned that a relatively small number of tree samples means that the timing of the glacier dynamics is not very well constrained. The lag of the glacier in response to climate change has been taken into account. The second example concerns δ 18 O measurements in a stalagmite from the Chinese Dongge cave (Wang et al., 2005). Stalagmites consist of CaCO3 which precipitates from the drip water when the pressure is reduced. The authors have shown that δ 18 O in this stalagmite is a proxy for the local precipitation rate. The stalagmite was dated using the U/Th technique and some tuning (<50 years) was done to match the 14 C curve. In Fig. 9 the δ 18 O and the record are both low-pass filtered with a 100 years cutoff. Again, there is clear evidence for a solar signal in the data. For example, the grand solar minimum around 2700 BP, one of the largest minima during the Holocene, shows up very clearly. This 2700 BP grand minimum is associated with evidence of climate change all over the globe (van Geel and Renssen, 1998). A spectral analysis of the data reveals the same periodicities that were found in the record (Table 1). This is another indication that the solar signal is imprinted in the precipitation rate. 7 Summary and Conclusions The Earth is an open system which is driven by energy coming almost exclusively from the Sun. Modern space based measurements of TSI show that the energy supply 214 J. Beer and K. McCracken 500 -0.5 18 0 0 O [MeV] -500 500 0.5 0 1000 2000 3000 4000 -0.5 18 0 [MeV] -500 0 5000 6000 7000 8000 O 0.5 9000 Age BP Fig. 9. Comparison of the δ 18 O measurements on a stalagmite from the Dongge cave in China (Wang et al., 2005) with the record from Fig. 6. Low values corresponding to low solar activity generally agree with high δ 18 O values interpreted as increased precipitation. Both data was first detrended by a polynomial of degree 3 and then low-pass filtered with a cut-off of 100 years and are shown as deviations from the long-term mean. from the Sun is subject to small changes (0.1%) which seem to be related to variations in the magnetic field of the Sun. This raises the important question to what extent solar variability affects the climate on Earth. Cosmogenic radionuclides provide the unique opportunity to reconstruct the history of the variability of the Sun, and its magnetic fields, over at least the past 10,000 years. The reconstruction of the solar modulation function is characterized by long-term changes as well as shortterm cyclicity (11-y Schwabe cycle). Other typical periodicities are 2200, 208, and 87 years. A special feature of solar variability are the so-called grand minima, periods when the solar activity is strongly reduced which leads to an almost complete absence of sunspots (only confirmed for the Maunder Minimum). A comparison of the solar modulation function with climate records points to a relationship between solar variability and climate forcing. Taking into account Evidence for Solar Forcing 215 that the Sun is just one forcing factor among others (volcanic, internal, greenhouse since the 20th century); that the climate response is spatially heterogeneous; and that there is some uncertainty in the time scales, the case for solar forcing looks promising. Evidence is strengthened by new high-precision records, together with GCM modeling which shows that the climate system is very sensitive to solar forcing (Ammann et al., 2007). The modern space age has shown us that there is a close relationship between the strength of the IMF, and TSI. Further still, we now have the ability to invert the cosmogenic data itself, or the modulation function , to provide estimates of the time dependence of the IMF far into the past. Such reconstructions indicate that the sunspot minimum value of the IMF near Earth has been lower (to ∼1 nT) and higher (to ∼8 nT) compared to 5.2 nT in 1976, 1968, and 1997. That is, the means now exists to (1) extrapolate the observed relationship between TSI and IMF, together with the estimated dependence of the IMF, to provide TSI as a function of time for the past 10,000 years for input to climate models, and (2) use the same process to test non-linear relationships between TSI and IMF. Acknowledgments. This work was supported by the International Space Science Institute (ISSI) and the Swiss National Science Foundation. References Abbot, C. G., The solar constant of radiation, Annual Report, 319 pp., Smithonian Institution, 1910. Ammann, C. 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